Sequence proof

Apr 2010
30
0
Can anyone give an \(\displaystyle \epsilon\) - N proof that the sequence:

xn = \(\displaystyle {\frac {2\,{n}^{2}+3}{4\,{n}^{2}+1}} \)

tends to 1/2?

Also more generally, give the \(\displaystyle \epsilon\) - N proof that the sequence {xn} n=1... infinity tends to x
 

Plato

MHF Helper
Aug 2006
22,461
8,633
If \(\displaystyle 0 < \varepsilon < 1\) let \(\displaystyle n > \frac{{\sqrt {\frac{5}{{2\varepsilon }} - 1} }}{2}\).
 
Apr 2010
30
0
Ok, i worked it through and i can understand that answer.

Im having trouble with the general proof however?